Integrability of a family of clean SYK models from the critical Ising chain

TL;DR

This paper demonstrates the integrability of a family of SYK models with uniform p-body interactions by deriving their R-matrix and transfer matrices, revealing a surprising connection to the critical transverse-field Ising chain.

Contribution

It establishes the integrability of certain SYK models and links them to the critical Ising chain through the R-matrix, providing exact solutions and spectral properties.

Findings

Derived the R-matrix of the SYK models

Connected SYK models to the critical Ising chain

Obtained exact eigenspectra and eigenstates

Abstract

We establish the integrability of a family of Sachdev-Ye-Kitaev (SYK) models with uniform $p$-body interactions. We derive the R-matrix and mutually commuting transfer matrices that generate the Hamiltonians of these models, and obtain their exact eigenspectra and eigenstates. Remarkably, the R-matrix is that of the critical transverse-field Ising chain. This work reveals an unexpected connection between the SYK model, central to many-body quantum chaos, and the critical Ising chain, a cornerstone of statistical mechanics.